4 step by step on solving linear equations

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Presentation transcript:

4 step by step on solving linear equations Make sure to do this on a separate sheet of paper before you click for the answers.

Things you need to know before we get in to the problem…. Transformations that produce equivalent equations. Addition property of equality: add the same number to both sides: if a = b then a + c=b= c. Subtraction property of equality subtract the same number from both sides: if a=b then a –c = b-c Multiplication property of equality Multiply both sides by the same nonzero number: if a =b and c is not equal to 0, then ac=bc. Division property of equality divide both sides by the same nonzero number if a=b and c is not equal to 0 than a/c=b/c Goal 1: solving a linear equation. An equation is a statement in which two expressions are equal. A linear equation in one variable is an equation that can be written in the form ax=b where a and b are constants and a is not equal to 0.

STEP BY STEP ……. Ex 1) 3/7x+9=15 Solution Your goal is to isolate the variable on one side of the equation 1st step: 3/7x+9=15 write original equation 2nd step: 3/7x=6 subtract 9 from each side. 3rd step: x=7/3(6 Multiply each side by 7/3, the reciprocal of 3/7. 4th step: x= 14 simplify Checking : check x = 14 in the original equation. 3/7(14)+9= 15 substitute 14 for x 15 = 15 solution checks

Step by step 2… Solving an equation with a variable on both sides. Solve 5n+11=7n-9 write original equation 11=2n-9 subtract 5n from each side. 20=2n add 9 to each side 10=n divide each side by 2. The solution is 10. check this in the original equation.

Step by step 3 Using the distributive property Solve 4(3x-5)=-2(-x+8)-6x 4(3x-5)=-2(-x+8)-6x write original equation 12x-20=2x-16-6x distributive property 12x-20=-4x-16 combine like terms. 16x-20=-16 add 4x to each side 16x=4 add 20 to each side X=1/4 divide each side by 16 The solution is 1/4 . Check this in the original equation.

Step by step 4 Solving an equation with fractions Solve 1/3x+1/4=x-1/6 1/3x+1/4=x-1/6 write the original solution 12(1/3x+1/4)=12(x-1/6) multiply each side by the LCD, 12 4x+3=12x-2 distributive property 3=8x-2 subtract 4x from each side 5 = 8x add 2 to each side 5/8 =x divide each side by 8 The solution is 5/8. check this in the original equation.